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UI Examples

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What is a subset?

Technical Answer: Set A is a of a Set B if and only if elements of A are also elements of B
In Other Words ...
There are two ways to be a subset
1) All the elements in Set A in Set B
OR
2) Set A has the elements as B

Subsets in Pictures

All elements of Set A are contained in Set B :
picture of subset
Set A has the exact same elements as Set B
diagram of subset

Subset Notation

$ \subseteq $ is the symbol for subset
Notation Meaning
A $\subseteq$ B "A is the subset of B"
B $\subseteq$ A "B is the subset of A"

Examples

1) Is Set A = { 2,4,6} a subset of B = {1, 2 , 3, 4, 5, 6 } Yes
no
2) Is Set A = {10, 15,20} a subset of B = {10,20,30,40 } Yes
no
3) Is $A=\{x: x \in \mathbb{Q}\}$ a subset of $B=\{x=\frac{1}{2},\frac{2}{3},\frac{3}{4},\cdots\}$? Yes
no
4) Is $A=\{x: x \in \mathbb{R}\}$ a subset of $B=\{x: x \in \mathbb{Q}\}$? Yes
no
5) Is set P = {} a subset of set M ={0,1,4,9,25,36}? Yes
no
6) Is $A=\{x: x \in \mathbb{Z^+}\}$ a subset of $B=\{x: x \in \mathbb{N}\}$? Yes
no
7) Is $A=\{x: x \in \mathbb{N}\}$ a subset of $B=\{x: x \in \mathbb{Z^+}\}$? Yes
no

Key Ideas

I. a set is a subset of itself
II. $\varnothing$ is a of every set
III. If A $\subseteq$ B and B $\subseteq$ A then
Based on this last definition are A = {1,2,3,4,5,6,7 } and B = {x|x< 7 and $ x \in \mathbb{N} \ $} equal? Yes
no

Practice Problems

1) Is {y } $ \subseteq $ {y}? Yes
no
2) Is Set A = { y } $ \in Set B= $ {y {y} }? Yes
no
3) Is Set A = {y} $ \subseteq Set B= $ { y , {y} }? Yes
no